General Balanced Random Effects Model
In previous chapters, we have considered random effects models for various crossed and nested designs with equal numbers in all cells and subclasses, and which are called balanced complete models. In this chapter, we present a unified treatment of balanced random effects models in terms of the so-called general linear model.
KeywordsVariance Component Unbiased Estimator Confidence Coefficient Exact Confidence Interval Approximate Confidence Interval
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- K. A. Brownlee (1965), Statistical Theory and Methodology in Science and Engineering, 2nd ed., Wiley, New York.Google Scholar
- R. K. Burdick and F. A. Graybill (1992), Confidence Intervals on Variance Components, Marcel Dekker, New York.Google Scholar
- G. Casella and R. L. Berger (2002), Statistical Inference, 2nd ed., Duxbury, Pacific Grove, CA.Google Scholar
- R. Das and B. K. Sinha (1987), Robust optimum invariant unbiased tests for variance components, in T. Pukkila and S. Puntanen, eds., Proceedings of Second International Tampere Conference on Statistics, University of Tampere, Tampere, Finland, 317–342.Google Scholar
- F. A. Graybill (1961), An Introduction to Linear Statistical Models, Vol. I, McGraw-Hill, New York.Google Scholar
- F. A. Graybill (1976), Theory and Application of the Linear Model, Duxbury, North Scituate, MA.Google Scholar
- K. M. S. Humak (1984), Statistische Methoden dwe Modellbildung III: Statistische Inferenzfur Kovarianzparameter, Akademia-Verlag, Berlin.Google Scholar
- E. L. Lehmann and H. Scheffé (1950), Completeness, similar regions and unbiased estimation, Sankhyā, 10, 305–340.Google Scholar
- T.-F. C. Lu (1985), Confidence Intervals on Sums, Differences and Ratios of Variances Components, Ph.D. dissertation, Colorado State University, Fort Collins, CO.Google Scholar
- T. Mathew, B. K. Sinha, and B. C. Sutradhar (1992), Nonnegative estimation of variance components in general balanced mixed models, in A. Md. E. Saleh, ed., Nonparametric Statistics and Related Topics, Elsevier, New York, 281–295.Google Scholar
- H. Raiffa and R. Schlaifer (1961), Applied Statistical Decision Theory, Harvard University Press, Cambridge, MA.Google Scholar